What is the Least Common Multiple of 12208 and 12216?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 12208 and 12216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12208 and 12216, than apply into the LCM equation.

GCF(12208,12216) = 8
LCM(12208,12216) = ( 12208 × 12216) / 8
LCM(12208,12216) = 149132928 / 8
LCM(12208,12216) = 18641616

Least Common Multiple (LCM) of 12208 and 12216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12208 and 12216. First we will calculate the prime factors of 12208 and 12216.

Prime Factorization of 12208

Prime Factorization of 12216

Now multiplying the highest exponent prime factors to calculate the LCM of 12208 and 12216.

LCM(12208,12216) = 2⁴ × 7¹ × 109¹ × 3¹ × 509¹
LCM(12208,12216) = 18641616